Specifically, a compile-time dependency is a module which needs to be loaded in order for a compile-check to work. A run-time dependency is one that only required to be loaded at run time.
That isn't very different than solving the halting problem, isn't it? Suppose a module "Dependency::Checker" exists, which exports a subroutine runtime_dependency that does what it says: 
package Foo;
use Dependency::Checker 'runtime_dependency';
use LWP::UserAgent;
sub make_agent {LWP::UserAgent->new}
BEGIN {
    make_agent() if runtime_dependency("LWP::UserAgent");
}
1;

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What will happen?

In reply to Re: use: distinguishing compile-time vs run-time dependencies by JavaFan
in thread use: distinguishing compile-time vs run-time dependencies by perl5ever

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